Transcript 9.1 Adding and Subtracting Polynomials • A monomial is an expression that is a number, a variable, or a product of a.

9.1 Adding and Subtracting Polynomials
• A monomial is an expression that is a number,
a variable, or a product of a number and one or
more variables.
– Ex.
12
y
-5x2y
• The degree of a monomial is the sum of the
exponents of its variables. For a nonzero
constant, the degree is 0. Zero has no degree.
Degree of a Monomial
• Find the degree of each monomial.
a. 2
x
Degree: 1
3
b.
2
7x y
3
Degree: 5
c. -4
Degree: 0
Polynomials
• A polynomial is a monomial or the sum or
difference of two or more monomials.
3x4 + 5x2 – 7x + 1
Degree: 4
2
1 0
• Standard form of a polynomial – the degrees
of its monomial terms decrease from left to
right.
• The degree of a polynomial in one variable is
the same as the degree of the monomial with
the greatest exponent.
– The degree of 3x4 + 5x2 – 7x + 1 is 4.
Names of Polynomials
Polynomial
Degree
Name Using
Degree
Number of
Terms
Name Using
Number of
Terms
7x + 4
1
Linear
2
binomial
3x2 + 2x + 1
2
Quadratic
3
Trinomial
4x3
3
Cubic
1
Monomial
9x4 + 11x
4
Fourth
Degree
2
Binomial
5
0
Constant
1
Monomial
Classifying Polynomials
• Write each polynomial in standard form. Then
name each polynomial based on its degree and
the number of its terms.
a. 5 – 2x
-2x + 5
linear binomial
b. 3x4 – 4 + 2x2 + 5x4
3x4 + 5x4 + 2x2 – 4
8x4 + 2x2 – 4
fourth degree trinomial
Adding Polynomials
• Simplify (4x2 + 6x + 7) + (2x2 – 9x + 1).
Method 1 – add vertically
4x  6x  7
2
2x  9x  1
2
6 x  3x  8
2
Method 2 – add horizontally – group like terms
(4 x  6 x  7)  (2 x  9 x  1)
2
2
 (4 x2  2 x2 )  (6 x  9 x)  (7  1)
 6 x  3x  8
2
Subtracting
Polynomials
3
2
3
2
• Simplify (2x + 5x – 3x) - (x – 8x + 11).
Method 1 – subtract vertically
2 x  5x  3x
3
2
( x  8x  11)
3
2
2 x  5x  3x
3
2
 x3  8x2 11)
x  13x  3x  11
3
2
Method 2 – subtract horizontally
2 x  5x  3x  x  8x  11
3
2
3
2
 (2 x  x )  (5x  8x )  3x  11
3
3
2
2
 x  13x  3x  11
3
2
More Practice!!!!
• Textbook – p. 459 #2 – 38 even.
• Homework – finish textbook problems.